Astm e 2175 01 (2013)

Designation E2175 − 01 (Reapproved 2013) Standard Practice for Specifying the Geometry of Multiangle Spectrophotometers1 This standard is issued under the fixed designation E2175; the number immediate[.]

Designation: E2175−01 (Reapproved 2013)

Standard Practice for

This standard is issued under the fixed designation E2175; the number immediately following the designation indicates the year of

original adoption or, in the case of revision, the year of last revision A number in parentheses indicates the year of last reapproval A

superscript epsilon (´) indicates an editorial change since the last revision or reapproval.

INTRODUCTION

The appearance of metallic coatings and plastics usually depends on the directions of illumination and viewing, a phenomenon called “gonioappearance.” This phenomenon is also observed with other

materials, such as lustrous textiles and materials containing pearlescent or interference pigments The

characteristic appearance of most such materials is accentuated by directional illumination, such as

that provided by the sun on a clear day or a small lamp at night The variation in color, as a function

of geometry, is usually measured by spectrophotometry with several specified sets of geometric

conditions Measurement of this kind, at a few selected angles, is called “multiangle

spectrophotometry,” as distinguished from measurement over a broad range of angles, which is called

“goniospectrophotometry.” Spectrophotometric aspects of these measurements, including spectral

resolution and linearity of photometric scales, are treated in other standards, including PracticeE308

and PracticeE1164 PracticeE1767provides practice for specifying the geometry of measurements

Retroreflectors exhibit a special kind of gonioappearance, which is treated in other ASTM documents

The present document provides standard practice for specifying influx and efflux angles, angular

selectivity, spatial distributions of illuminators and receivers, and angular aspects of standardizing the

photometric scale, that are peculiar to multiangle spectrophotometry Directional illumination

emphasizes the gonioappearance of most materials, but when interference pigments are used, such as

those used in ink to mark paper currency, the effect is observed with diffuse illumination and varying

angles of viewing, so these materials are also measured with diffuse illumination

1 Scope

1.1 This practice provides a way of specifying the angular

and spatial conditions of measurement and angular selectivity

of a method of measuring the spectral reflectance factors of

opaque gonioapparent materials, for a small number of sets of

geometric conditions

1.2 Measurements to characterize the appearance of

retrore-flective materials are of such a special nature that they are

treated in other ASTM documents and are not included in the

scope of this standard

1.3 This standard does not purport to address all of the

safety concerns, if any, associated with its use It is the

responsibility of the user of this standard to establish

appro-priate safety and health practices and determine the

applica-bility of regulatory limitations prior to use.

2 Referenced Documents

2.1 ASTM Standards:2

E284Terminology of Appearance E308Practice for Computing the Colors of Objects by Using the CIE System

E1164Practice for Obtaining Spectrometric Data for Object-Color Evaluation

E1767Practice for Specifying the Geometries of Observa-tion and Measurement to Characterize the Appearance of Materials

3 Terminology

3.1 For definitions of appearance terms used in this practice, refer to TerminologyE284

4 Significance and Use

4.1 This practice is for the use of manufacturers and users of instruments to measure the appearance of gonioapparent

1 This practice is under the jurisdiction of ASTM Committee E12 on Color and

Appearance and is the direct responsibility of Subcommittee E12.03 on Geometry.

Current edition approved Oct 1, 2013 Published October 2013 Originally

approved in 2001 Last previous edition approved in 2008 as E2175 – 01 (2008).

DOI: 10.1520/E2175-01R13.

2 For referenced ASTM standards, visit the ASTM website, www.astm.org, or

contact ASTM Customer Service at service@astm.org For Annual Book of ASTM

Standards volume information, refer to the standard’s Document Summary page on

the ASTM website.

Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959 United States

materials, those writing standard specifications for such

instruments, and others who wish to specify precisely the

geometric conditions of multiangle spectrophotometry A

prominent example of industrial usage is the routine

applica-tion of such measurements by material suppliers and

automo-bile manufacturers to measure the colors of metallic paints and

plastics

5 Components of Apparatus

5.1 The apparatus shall consist of one or more illuminators

and one or more spectrometric receivers at fixed or adjustable

angles with respect to a reference plane, a means of positioning

specimens in a reference plane, a means of indicating the area

on the specimen to be measured, shielding to avoid stray light,

and a means of displaying spectral or colorimetric data and/or

communicating such data to a data-recorder or computer (The

terms “light,” “illuminator,” “illumination,” and “illuminance”

are used here for simplicity, though the corresponding terms

“radiant power,” “irradiator,” “irradiation,” and “irradiance”

would be more accurate when the incident flux includes

ultraviolet flux, as is necessary if the appearance of a

fluores-cent material is measured.)

6 Geometric Types of Apparatus

6.1 The geometric configuration of the instrument may be

uniplanar, annular, circumferential, or diffuse In all cases, the

specimen is taken to be a flat surface lying in a plane called the

“reference plane,” which is designated the x, y plane When

there is a single directional illuminator, the x direction is the

direction of the projection of the axis of the incident beam on

the reference plane If there are several directional illuminators

or a single diffuse illuminator, the direction of the x-axis must

be selected and specified The area of the reference plane on

which measurements are made is called the “sampling

aper-ture” and the center of that area is designated the origin, o, of

the geometric space used to specify the configuration The

normal to the sampling aperture, at the origin, is the -z-axis

Angles subtended at the origin and measured from that normal

are called “anormal angles.” The specular direction is the

direction of the beam from a directional illuminator after

specular reflection by an ideal plane mirror at the sampling aperture Angles subtended at the origin and measured from the specular direction are called“ aspecular angles” and are posi-tive in sign when measured in the direction toward the normal The normal and the axis of a directional illuminator define a plane, known as the “plane of incidence.” The specular direction necessarily lies in that plane

6.1.1 To facilitate simple and precise geometric specifica-tion of the sampling aperture, it shall be either circular or rectangular

6.1.2 To facilitate simple and precise geometric specifica-tion of direcspecifica-tional influx or efflux distribuspecifica-tions, they shall be either conical or pyramidal For purposes of describing geom-etry by functional notation, a diffuse distribution may be considered a conical distribution centered on the normal and having a half angle of 90 degrees

6.1.3 In a uniplanar configuration, a directional illuminator

is used, the axes of the receivers lie in the plane of incidence, and their positions are specified by aspecular angles A uniplanar configuration is illustrated inFig 1 To simplify the figure, only one receiver is shown

6.1.3.1 For a conical influx distribution, the flux incident on the origin comes from an area of a directional illuminator uniformly filling a circle on a plane normal to the beam For a conical efflux distribution, flux from the origin is uniformly collected and evaluated over an area of the receiver that is a circle on a plane normal to the beam A uniplanar configuration with conical influx and efflux distributions is illustrated inFig

2 To simplify the figure, only one receiver is shown 6.1.3.2 For a pyramidal influx distribution, flux incident on the origin comes from an area of a directional illuminator uniformly filling a rectangle on a plane normal to the beam For

a pyramidal efflux distribution, flux from the origin is uni-formly collected and evaluated over an area of the receiver that

is a rectangle on a plane normal to the beam A pyramidal configuration can be used to subtend a small angle in the plane

of incidence, to enhance angular selectivity, but have a large enough solid angle to provide adequate flux for reliable measurements A uniplanar configuration with pyramidal influx and efflux distributions is illustrated in Fig 3 To simplify the

FIG 1 Uniplanar Configuration

figure, only one receiver is shown and the angles δ and ε are

shown for the receiver, but not for the illuminator

6.1.4 In an annular configuration, the incident beam

uni-formly fills the space between two right-circular cones, with

their axes on the normal and apices at the origin An annular

configuration can be used to provide a flux distribution with a

small range of anormal angles, to enhance anormal angular

selectivity, but of large enough solid angle to provide adequate

flux for reliable measurements The nominal angle of an

annular distribution is the average of the half-angles of the two

defining cones For multiangle spectrophotometry, provision

must be made for several annular distributions with different

nominal angles The efflux distribution is a conical distribution

with its axis on the normal and its apex at the origin

6.1.5 A circumferential configuration approximates an

an-nular configuration, except that flux incident on the origin

comes from a ring of discrete directional illuminators, all

having their axes at the same anormal angle, but arrayed at

various azimuthal angles The nominal angle of incidence is

measured from the normal to the axes of the illuminators For

multiangle spectrophotometry, provision must be made for

illuminators at several different nominal angles A

circumfer-ential configuration with three illuminators is illustrated inFig

4 To simplify the figure, the angles κi, θi, and ηiare shown for the first illuminator only

6.1.5.1 The discrete illuminators shall all have the same nominal angle of incidence, for a given measurement 6.1.6 In a diffuse configuration, the incident flux is diffuse Ideally, the illuminator illuminates the sampling aperture at all angles within the hemisphere on the -z side of the reference plane, except those directions occupied by receivers The use

of an integrating sphere to produce uniform diffuse illumina-tion requires non-selective diffusing baffles to obscure the entrance port and the area on the sphere wall at which the flux entering the sphere is first reflected When diffuse illumination

is used, the receivers are all in one plane defined by the normal and having an arbitrarily designated x-axis The positions of the receivers are specified by anormal angles

6.2 Given a geometric configuration, the reverse geometry

is considered equivalent, if all other components of the instrument design are equivalent

7 Nominal Geometric Specifications

7.1 Angles for these specifications are customarily given in degrees

FIG 2 Uniplanar Configuration with Conical Influx and Efflux Distributions

FIG 3 Uniplanar Configuration with Pyramidal Influx and Efflux Distributions

7.2 Uniplanar Geometry:

7.2.1 The direction of a conical distribution is specified by

the angle θ subtended at the origin from the normal to the axis

of the distribution or the angle α subtended at the origin from

the specular direction to the axis of the distribution The extent

of a conical distribution is specified by the angle κ subtended

at the origin by the radius of the circular distribution at the

illuminator or receiver, with subscripts i and r indicating

illuminator and receiver, respectively (SeeFig 2.) When more

than one illuminator or receiver is involved, they are

distin-guished by alphabetic subscripts a, b, c, etc., the half-angles

being given symbols of the form κia, κib, κic, … and κra, κrb, κrc

…

7.2.2 A pyramidal distribution is specified by angles δ and ε,

where δ is the angle subtended at the origin from the central

axis of the distribution to the edge, measured in the direction

normal to the plane of incidence, and ε is the angle subtended

at the origin from the central axis of the distribution to the

edge, measured in the plane of incidence Subscript i and r

distinguish half-angles for the illuminator and receiver,

respec-tively Letter subscripts are added to identify multiple

distributions, as in the case of circular conical distributions

(SeeFig 3.)

7.3 An annular distribution is specified by a half-angle κi1or

κr1for the smaller of the two cones limiting the annulus and κi2

or κr2 for the larger of the two Subscripts a,b,c, etc are used

to distinguish multiple distributions, as in the case of conical

distributions, for example, κi1c The nominal angle of incidence

or angle of reflection is given the same symbol without the 1 or

2, for example κic (See Fig 4.)

7.4 A circumferential distribution is specified by the

anor-mal angle θ of the axes of the discrete illuminators, the conical

or pyramidal description of the discrete illuminators, and the

azimuthal positions of their axes with respect to some

identi-fied direction, considered the x direction.

7.5 A diffuse distribution is specified by specifying

directions, if any, from which illumination is excluded, other

than the obvious directions of receivers and necessary baffles

Excluded directions are specified in the same way as conical or

pyramidal influx or efflux distributions

8 Angular Selectivity

8.1 Angular selectivity is the degree to which the measured spectral quantity approaches the ideal value for the nominal angular geometry Precise characterization of the effective angular “slit-width” of the measurement system can be difficult, but the fraction of the angular illumination distribu-tion and the angular sensitivity distribudistribu-tion within specified angles can be determined by practical means

8.2 Ideally, flux incident on the origin should come from the nominal direction specified for the measurement At least

∆Eα% of the incident flux shall come from angles within ∆α1 degrees of the nominal direction All of the incident flux shall come from angles within ∆α2degrees of the nominal direction 8.3 Ideally, the sensitivity of a receiver should be limited to

the nominal direction A fraction ∆Sα% of the angular sensi-tivity distribution shall be within ∆α3degrees of the nominal direction All of the angular sensitivity distribution shall be within ∆α4degrees of the nominal direction

9 Tolerances

9.1 The objective is to have the sampling aperture uniformly illuminated Tolerances are specified for the departure from uniformity of the illuminance The nominal specified angular extents of influx and efflux distributions should not be confused with tolerances Tolerances are set on the specified boundaries The objective is to have the specified nominal angular extents

of influx and efflux distributions uniformly filled Tolerances are specified for the departure from uniformity

9.2 Angular tolerances are given the same symbols as nominal angles, preceded by the Greek delta symbol ∆, for example ∆κia, for a tolerance on the half-angle of conical influx distribution “a.” Upper tolerances are specified by +∆, lower tolerances are specified by -∆, and symmetric tolerances are specified by 6∆

9.3 The illuminance J at any place on the sampling aperture shall be within ∆Ja% of the mean illumination, when mea-sured with a circular radiometric scanning aperture having a

diameter ∆d % of the diameter of a circular sampling aperture

or measured with a square radiometric scanning aperture

FIG 4 Circumferential Configuration

having a side ∆w % of the smaller of the two dimensions of a

rectangular sampling aperture

N OTE1—The usual symbol for illuminance is E, but in colorimetry, ∆E

signifies total color difference, so to avoid confusion, the special symbol

J is used here for illuminance.

9.4 The sampling aperture shall be shielded from light other

than that from the illuminator used for measurement at the

specified angle The illuminance due to stray light from

extraneous sources or unintended light paths shall not exceed

∆E s% of that due to the intended light path

9.5 The luminance K of a directional illuminator, in the

direction of any point on the sampling aperture, shall not differ

more than ∆K % from the mean luminance, when measured

using a radiometer uniformly sensitive over a conic distribution

having a half angle κ % of the diameter of the half angle of the

illuminator or over a square-based pyramidal distribution, a

side of the square base being a specified percent of the smaller

of δ or ε

N OTE2—The usual symbol for luminance is L, but in colorimetry, ∆L

signifies lightness difference, so to avoid confusion, the special symbol K

is used here for luminance.

9.6 The luminance of an annular illuminator, in the direction

of any point on the sampling aperture, shall not differ more

than ∆K % from the mean luminance, when measured using a

radiometer uniformly sensitive over a conic distribution having

a half angle σ % of the difference in angles between the cones

defining the annular distribution

9.7 The sensitivity of a receiver S to light from any point on the sampling aperture shall be within ∆S a% of the mean sensitivity, when exposed to a constant test beam uniform over

a conic distribution having a half angle κ % of the diameter of the half angle of a conical receiver or over a square-based pyramidal distribution, a side of the square base being a specified percent of the smaller of δ or ε

10 Standardization of the Photometric Scale:

10.1 In most spectrophotometry, the geometry is singular and fixed and the white standard used to standardize the photometric scale of the instrument is placed at the sampling aperture, in place of the specimen to be measured In multi-angle spectrophotometry, there are several different geom-etries The white standard could be placed at the sampling aperture, be placed normal to the axis of the illuminator, be placed normal to the axis of the receiver, or be oriented in some other way The practice must be specified The most practical method is to place the white standard at the sampling aperture The manner of calibration of the white standard and the way the calibration data are applied to standardizing the multiangle measurement must be specified

11 Keywords

11.1 appearance; appearance difference; color; color differ-ence; color matching; geometry; gonioappearance; goniochro-matism; goniospectrophotometry; multiangle spectrophotom-etry; spectrophotometry

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